Not technically, it's a constitutional monarchy which means that while the queen is the official head of state she has no official power there. They have their own prime minister who acts like the American President.
No, Australia was independent in 1901.
This is a commonly used term for Australia in the UK.
they keep vermin under control
Both are colloquial terms for places. Down under is Australia and Blight is the UK or England.
It was allied to the UK and US.
There are no countries currently under British control. However, their are 14 territories throughout the world which are independent, but where ultimate control, particularly for defence, is the responsibility of the UK.
The dialling code from UK to Australia is 00 61.
Australia is a member of Commonwealth; Australia is formally dependent on UK because recognize Elisabeth as queen.
7,686,850 km2 for Australia, 244,101 km2 for the UK. So Australia is 31.49 times bigger than the UK.
Australia does not have a president, so no control.
They were ruled by the UK and won their independence from them on July 10, 1973.
At the time Australia was under British rule. So when the UK entered the war, Australian troops were also deployed. They fight for their king/queen, of Britain.